Further improved stability results for generalized neural networks with time-varying delays
This paper is concerned with a new Lyapunov–Krasovskii functional (LKF) approach to delay-dependent stability for generalized neural networks with time-varying delays (DNN). A new LKF is constructed by employing more information of the DNN. The state, the activation function and their ramifications...
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| Published in: | Neurocomputing (Amsterdam) Vol. 367; pp. 308 - 318 |
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| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
20-11-2019
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| Abstract | This paper is concerned with a new Lyapunov–Krasovskii functional (LKF) approach to delay-dependent stability for generalized neural networks with time-varying delays (DNN). A new LKF is constructed by employing more information of the DNN. The state, the activation function and their ramifications are introduced, and more cross terms of the activation function and their ramifications are included in the LKF. Moreover, the new LKF also makes best of the characteristic of the activation function. On the other hand, when estimating the derivative of the LKF, we take advantages of some equations and inequalities that reveal the relationship among the state, the activation function and their ramifications, employ advanced inequalities to deal with integrals arising from the derivative of the LKF, thus resulting in a tight upper bound of the derivative of the LKF. By checking the negative definiteness of the upper bound that is a quadratic function in the time-delay, a novel delay-dependent stability result is derived. Finally, three examples are given to illustrate the stability result is less conservative than some recently reported ones. |
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| AbstractList | This paper is concerned with a new Lyapunov–Krasovskii functional (LKF) approach to delay-dependent stability for generalized neural networks with time-varying delays (DNN). A new LKF is constructed by employing more information of the DNN. The state, the activation function and their ramifications are introduced, and more cross terms of the activation function and their ramifications are included in the LKF. Moreover, the new LKF also makes best of the characteristic of the activation function. On the other hand, when estimating the derivative of the LKF, we take advantages of some equations and inequalities that reveal the relationship among the state, the activation function and their ramifications, employ advanced inequalities to deal with integrals arising from the derivative of the LKF, thus resulting in a tight upper bound of the derivative of the LKF. By checking the negative definiteness of the upper bound that is a quadratic function in the time-delay, a novel delay-dependent stability result is derived. Finally, three examples are given to illustrate the stability result is less conservative than some recently reported ones. |
| Author | Feng, Zongying Shao, Hanyong Shao, Lin |
| Author_xml | – sequence: 1 givenname: Zongying surname: Feng fullname: Feng, Zongying organization: The Research Institute of Automation, Qufu Normal University, Rizhao 276826, China – sequence: 2 givenname: Hanyong surname: Shao fullname: Shao, Hanyong email: hanyongshao@163.com organization: The Research Institute of Automation, Qufu Normal University, Rizhao 276826, China – sequence: 3 givenname: Lin surname: Shao fullname: Shao, Lin organization: College of Electronic and Information Engineering, Shandong University of Science and Technology, Qingdao 266590, China |
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| CitedBy_id | crossref_primary_10_1109_TCYB_2020_3031087 crossref_primary_10_1016_j_amc_2023_128289 crossref_primary_10_1016_j_ins_2021_08_055 crossref_primary_10_1109_TNNLS_2022_3202799 crossref_primary_10_1016_j_neucom_2020_05_045 crossref_primary_10_1016_j_neucom_2021_01_098 crossref_primary_10_1016_j_ins_2023_03_041 crossref_primary_10_1109_TNNLS_2022_3159625 crossref_primary_10_1186_s13660_023_02973_7 crossref_primary_10_1016_j_jfranklin_2020_04_049 crossref_primary_10_1016_j_knosys_2022_109630 crossref_primary_10_1002_mma_9425 crossref_primary_10_3934_math_20231136 crossref_primary_10_1016_j_neucom_2020_02_059 crossref_primary_10_1016_j_amc_2020_125431 crossref_primary_10_1109_ACCESS_2021_3089374 crossref_primary_10_1016_j_neunet_2021_11_007 crossref_primary_10_1016_j_amc_2020_125631 crossref_primary_10_1080_21642583_2020_1858363 crossref_primary_10_1016_j_jfranklin_2024_106871 crossref_primary_10_1109_ACCESS_2023_3326715 crossref_primary_10_1007_s12555_022_0875_0 crossref_primary_10_1016_j_neucom_2020_07_021 crossref_primary_10_1016_j_neucom_2022_02_015 |
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